items should be partitioned in disjoint subsets (bins)‚ such that the total size in each bin is at most 1. The first fit heuristic scans the items one by one‚ and each item is assigned to the first bin that it can fit in. Prove that first-fit is a 2-approximation algorithm for bin packing. Hint. Bound from below the number of bins used by an optimal solution; and bound from above the number of bins used by first fit‚ using the observation that nearly all bins are at least half-full. 2. Suppose now that you
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(shortage) is assessed. We use stochastic programming to model this problem‚ and propose an optimal bundle-type algorithm to solve it. Furthermore‚ we develop some simple and effective approximation algorithms for several special cases. Extensive numerical experiments are conducted to show the effectiveness of the approximation algorithms‚ to compare the performance between the traditional production model and the postponement production model‚ and to examine the impact of parameters on the performances
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A Sensitivity Analysis of Retailer Shelf Management Models NORM BORIN California Polytechnic State University PAUL FARRIS University of Virginia A shelf management model was developed to assist retailers with the decision of which products to stock and how much space to allocate to those products. Due to the non-linearities in the formulation a closedfotm solution is not possible. Borin‚ et al. develop a search heuristic based on simulated annealing and compare the solution against
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Given : Approximation of FOPTD Model (a)Two Points Method [See Appendix-A for MATLAB Code] Figure (1): Process reaction curve using Matlab At 28.4%‚ t1 = 2.48s At 63.2%‚ t2 = 4.18s T = 1.5(t2 – t1) = 1.5(4.18-2.48)=2.55s L = 0.5(3t1-t2)=0.5(3*2.48-4.18)=1.63s Gain K=1 Approximated TF is : Gs=1e-1.63s2.55s+1 Verification of Two Point Method in Time domain and Frequency domain [See Appendix-A for MATLAB Code] Figure (2): Verification of Two Point Method in Time
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Student: Keila Dukuze Date: Feb/10/2013 Lab# 3 Section: 110 Pre-Lab Report Determining the Density of Various Liquids and Solids The purpose of this experiment is to determine the weight (density) of certain liquids and solids in chemistry. These liquids include; Water‚ Hexane‚ Carbon Tetrachloride‚ and solids include; Copper‚ Zinc‚ Lead and‚ Aluminum. It’s important to know the weight of these products so you can properly conduct experiments and make clear observations. Different
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CAMBRIDGE INTERNATIONAL EXAMINATIONS Compiled by Imran Mirza MSc Physics‚ PGCC‚ Scoland‚ Uk Planning Analysis And Evaluation A-level Physics This booklet covers CIE A Level Physics Paper 5 By Imran Mirza 2009-2011 Exam tips for Planning‚ Analysis and Evaluation paper By Imran Mirza Don’t rush........ Three golden rules........ 1. Read the question 2. READ the question 3. Answer the question Make sure that you do not do what so many students do......they see a ’key c word like ’magnetic flux’
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Date File 1 Chapter One 1) Determine whether the evaluated group is a population or a sample. a) Based on a randomly selected group of 500 patients with high cholesterol‚ it was found that 67% have heart disease. Is this a population or a sample; explain your answer. Population‚ because it is the study of a number of people for a particular study. b) An investigation of 150 randomly selected local restaurants concluded that 42% of local restaurants have serious health code violations. Is
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Outline MODI METHOD How to Use the MODI Method Solving the Arizona Plumbing Problem with MODI VOGEL’S APPROXIMATION METHOD: ANOTHER WAY TO FIND AN INITIAL SOLUTION DISCUSSION QUESTIONS PROBLEMS T4-2 CD TUTORIAL 4 THE MODI AND VAM METHODS OF SOLVING TRANSPORTATION PROBLEMS This tutorial deals with two techniques for solving transportation problems: the MODI method and Vogel’s Approximation Method (VAM). MODI METHOD The MODI (modified distribution) method allows us to compute improvement indices
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of techniques that use successive approximations to obtain more accurate solutions to a linear system at each step. Rate of convergence: In numerical analysis‚ the speed at which a convergent sequence approaches its limit is called the rate of convergence. Although strictly speaking‚ a limit does not give information about any finite first part of the sequence‚ this concept is of practical importance if we deal with a sequence of successive approximations for an iterative method‚ as then typically
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Zu Chongzhi’s lifetime and achievements Zu Chongzhi’s ancestry was from modern Baoding‚ Hebei. To flee from the ravage of war‚ his grandfather Zu Chang moved to the Yangtze. Zu was born in Jiankang in 429 A.D. Both his grandfather and his father all worked in the government of science and engineering. As a result‚ he started learning astronomy and mathematics from a very young age. He didn’t have any other hobbies‚ he only interested in his studies of science. He passed away in 500 A.D. He lived
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